WP Stats problem - Variable change

[ammarjavaid007]

Hey,

I was doing this stats problem and was wondering how the answer would change if one of the variables changed.

In this problem we are given the mean and median (where median > mean) for a set of 7 numbers and are told that that largest number in the set is 14 more than 4 times the smallest number. The question wants to know the max the largest number can be. It was clear than in order to get the max number I had to max the value of x (the smallest number in the set). Since the mean was lower than the median I made the first 3 numbers in the set = to x so that:

x, x, x, median, median, median, 4x+14

Therefore, Sum/7 = mean

This would maximize the value of x.

What I want to know is whether I would arrange the numbers differently if the given mean was larger than the median? How would it affect the question?

I know I'm not allowed to refer to the OG on the forum so I've tried my best to explain this problem in my own words. IF anyone can help me, that would be great.

Thanks.

[RonPurewal]

The problem is, unfortunately, that you're still asking about a question from a prohibited source.
Sure, you may have changed the exact wording, but (as you seem to have admitted in this thread) the actual math problem hasn't been altered at all.

If you want to do this here, you'll have to cook up a substantively different problem that works in the same way as the original. That may not be the easiest thing in the world to do; for instance, this problem is probably sensitive to the exact numbers provided in the original, and may change substantially if those numbers are changed.
But, at the end of the day, a prohibited source is still a prohibited source, so you've got to try.

[ammarjavaid007]

Okay Ron,

Hmm ill just get to the point of what I want to know, not just for this question, but for any question regarding a set of integers.

I'm given the mean and median of an odd set of lets say 9 or 15 integers and want to minimize the value for the first integer in the set. Would my tactic for calculating the minimum value change if:
- mean < median
- mean > median

Or would it stay the same. Please let me know.

Thanks.

[RonPurewal]

Okay Ron,

Hmm ill just get to the point of what I want to know, not just for this question, but for any question regarding a set of integers.

I'm given the mean and median of an odd set of lets say 9 or 15 integers and want to minimize the value for the first integer in the set. Would my tactic for calculating the minimum value change if:
- mean < median
- mean > median

Or would it stay the same. Please let me know.

Thanks.

I don't see why these would have anything to do with each other.

* If the mean is given, then you'll probably just use it to calculate the sum of all the numbers in the set, and then throw it away.

* The median is the middle value. Because you have to keep it in the middle, it somewhat restricts your ability to make the other numbers in the set bigger or smaller.
If there were no restrictions on the median at all, then maximizing one value would mean bringing all the other values down to the minimum possible. (E.g., if you have seven different integers that have to add up to 100, then, if there are no restrictions, you can make six of the numbers 1, 2, 3, 4, 5, and 6, and then the seventh number is 100 minus all those. If there's a restriction on the median, you won't be able to make all the numbers so small.)

[RonPurewal]

In general, you will not have to know any complex relationships at all on this test.
None.

If you are trying to memorize rules for what to do if "mean > median" vs. if "mean < median", that's already way, waaaaayyyy too complicated for the gmat.

These problems do ingenious things, but always, always, always with basic elements only.

[ammarjavaid007]

Gotcha,

Thanks allot Ron. Im not trying to memorize anything, I just though of a confusing concept in my head and got a little carried away.

Thanks for clarifying.

[RonPurewal]

Sure.